code: def test_expint():
      x = Symbol("x")
      a = Symbol("a")
      u = Symbol("u", polar=True)
  
      # TODO LT of Si, Shi, Chi is a mess ...
      assert laplace_transform(Ci(x), x, s) == (
          -log(1 + s**2) / 2 / s,
          0,
          True,
      )
      assert laplace_transform(expint(a, x), x, s, simplify=True) == (
          lerchphi(s * exp_polar(I * pi), 1, a),
          0,
          re(a) > S.Zero,
      )
      assert laplace_transform(expint(1, x), x, s, simplify=True) == (
          log(s + 1) / s,
          0,
          True,
      )
      assert laplace_transform(expint(2, x), x, s, simplify=True) == (
          (s - log(s + 1)) / s**2,
          0,
          True,
      )
      assert inverse_laplace_transform(
          -log(1 + s**2) / 2 / s, s, u
      ).expand() == Heaviside(u) * Ci(u)
      assert inverse_laplace_transform(
          log(s + 1) / s, s, x, simplify=True
      ).rewrite(expint) == Heaviside(x) * E1(x)
      assert (
          inverse_laplace_transform(
              (s - log(s + 1)) / s**2, s, x, simplify=True
          )
          .rewrite(expint)
          .expand()
          == (expint(2, x) * Heaviside(x))
          .rewrite(Ei)
          .rewrite(expint)
          .expand()
      )
  
imports: from sympy.integrals.laplace import laplace_transform, inverse_laplace_transform, LaplaceTransform, InverseLaplaceTransform, _laplace_deep_collect, laplace_correspondence, laplace_initial_conds
  from sympy.core.function import Function, expand_mul
  from sympy.core import EulerGamma, Subs, Derivative, diff
  from sympy.core.exprtools import factor_terms
  from sympy.core.numbers import I, oo, pi
  from sympy.core.relational import Eq
  from sympy.core.singleton import S
  from sympy.core.symbol import Symbol, symbols
  from sympy.simplify.simplify import simplify
  from sympy.functions.elementary.complexes import Abs, re
  from sympy.functions.elementary.exponential import exp, log, exp_polar
  from sympy.functions.elementary.hyperbolic import cosh, sinh, coth, asinh
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.elementary.piecewise import Piecewise
  from sympy.functions.elementary.trigonometric import atan, cos, sin
  from sympy.logic.boolalg import And
  from sympy.functions.special.gamma_functions import lowergamma, gamma, uppergamma
  from sympy.functions.special.delta_functions import DiracDelta, Heaviside
  from sympy.functions.special.singularity_functions import SingularityFunction
  from sympy.functions.special.zeta_functions import lerchphi
  from sympy.functions.special.error_functions import fresnelc, fresnels, erf, erfc, Ei, Ci, expint, E1
  from sympy.functions.special.bessel import besseli, besselj, besselk, bessely
  from sympy.testing.pytest import slow, warns_deprecated_sympy
  from sympy.matrices import Matrix, eye
  from sympy.abc import s
label_desc: Use image node_id 4 for calling a global function with example usage: test_expint() without return types